Analytical Solution for the Time-Fractional Telegraph Equation
We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate st...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2009/890158 |
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| _version_ | 1832567165450977280 |
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| author | F. Huang |
| author_facet | F. Huang |
| author_sort | F. Huang |
| collection | DOAJ |
| description | We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series. |
| format | Article |
| id | doaj-art-3fb8689896da498fbe0a7c8700ec7434 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3fb8689896da498fbe0a7c8700ec74342025-02-03T01:02:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422009-01-01200910.1155/2009/890158890158Analytical Solution for the Time-Fractional Telegraph EquationF. Huang0Department of Mathematics, School of Sciences, South China University of Technology, Guangzhou 510641, ChinaWe discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.http://dx.doi.org/10.1155/2009/890158 |
| spellingShingle | F. Huang Analytical Solution for the Time-Fractional Telegraph Equation Journal of Applied Mathematics |
| title | Analytical Solution for the Time-Fractional Telegraph Equation |
| title_full | Analytical Solution for the Time-Fractional Telegraph Equation |
| title_fullStr | Analytical Solution for the Time-Fractional Telegraph Equation |
| title_full_unstemmed | Analytical Solution for the Time-Fractional Telegraph Equation |
| title_short | Analytical Solution for the Time-Fractional Telegraph Equation |
| title_sort | analytical solution for the time fractional telegraph equation |
| url | http://dx.doi.org/10.1155/2009/890158 |
| work_keys_str_mv | AT fhuang analyticalsolutionforthetimefractionaltelegraphequation |